1. Sub-structure of Dark-Matter Halos
Lecture
Sub-structure of Dark-Matter Halos

2. N-body simulation of Halo Formation

5. Origin of Halo Density Profile?
=1 2 3 r ρ
Varying slope -α
Navarro & Taylor: r
Hayashi, Navarro et al.

6. Phase-Space Density Vlasov eq. Poisson eq. Distribution function of f:
V(f)df = volume of phase space occupied by f in the range (f,f+df)

7. Measuring f(x,v) using an adaptive “grid” Delaunay Tesselation
particle i
Arad, Dekel & Klypin

8. PDF of Phase-Space Density
v∝f-2.5
V(f) f
Arad, Dekel & Klypin

9. Dwarf
v(f) f

10. Dwarf
v(f) f

11. Cluster
v(f) f

12. PDF of Phase-Space Density
V(f)
109Mʘ
1012Mʘ
1015Mʘ f
Arad, Dekel & Klypin

13. V(f) related to ρ(r)? if
e.g., spherical & isotropic

14. Halo Phase-Space Density
Real Density
Phase-Space Density

15. Halo Phase-Space Density
Real Density
Phase-Space Density

16. Profiles in Real Space and Phase Space
f(r)
ρ(r)
radius
radius

17. Is v(f)∝f-2.5 determined by substructure?
ΛCDM
No short waves
Moore et al.
Real-Space Density

18. Phase-Space density
ΛCDM
No short waves

19. Phase-Space Density Profile
ΛCDM
No short waves
f(r)
f(r)
radius
radius

20. Same power law v(f)?
no short waves
v∝f-3.2
ΛCDM
v∝f-2.5
v(f) f

21. Additive Contribution of Subhalos
v∝f-2.5
each subhalo is not a power law

22. The Two Most Massive Subhalos
v∝f-2.5

23. Background Halo – Subhalos Removed
The background halo is steeper
v∝f-3
v∝f-2.5
leftover substructure

24. Background Halo
real space phase space

25. Adding up Sub-halos ρ(r)→v(f) f-2 halo mass function: v∝f-2.5
v(f) from a universal density profile
ρ(r)→v(f)
f-2.8
f-2
v∝f-2.5
halo mass function:
sum of halos
f v(f)
Scaling of halos: f
subs/host
Boylan-Kolchin, Ma, Arad, Dekel f

26. Tentative Conclusions
In hierarchical clustering, robust PDF: v(f)∝f-2.5 doesn’t depend on power-spectrum slope, or on method of simulation
The power-law v(f) is driven by substructure. How exactly? Yet to be understood !
Phase-space density is a unique tool for studying substructure and its evolution
Adding up small CDM halos leads to v(f)∝f-2.5 ? How robust? How dependent on subhalo density profile and mass function?

27. Satellite merging into a halo
apo 0
peri 1
apo 1
apo 2
apo 3
final
Dekel, Devor & Hetzroni 2003